Correlation functions of disorder fields and parafermionic currents in ZN Ising models

We study the correlation functions of parafermionic currents and disorder fields in the ZN symmetric conformal field theory perturbed by the first thermal operator. Following the ideas of Al Zamolodchikov (Zamolodchikov 1991 Nucl. Phys. B 348 619, Zamolodchikov 1990 Nucl. Phys. B 342 695 and Zamolodchikov 1995 Int. J. Mod. Phys. A 10 1125), we develop for the correlation functions the conformal perturbation theory at small scales and the form factors' spectral decomposition at large ones. For all N, there is an agreement between the data at the intermediate distances. We consider the problems arising in the description of the space of scaling fields in perturbed models, such as null vector relations, equations of motion and a consistent treatment of fields related by a resonance condition.